Archimedes discovers the principle of buoyancy, which states that an object immersed in a fluid experiences an upward force equal to the weight of the fluid displaced. Legend attributes this discovery to him exclaiming 'Eureka!' (I have found it!) while in a bath.

Archimedes invents the Archimedes screw, a device used for raising water efficiently. This invention, likely developed for irrigation or drainage, remains in use in some parts of the world even today.

During the Siege of Syracuse, Archimedes designs and builds a variety of innovative defensive weapons to defend the city against the Roman invaders. These included catapults with a long range and devices to capsize Roman ships.

Archimedes is credited with inventing the 'Claw of Archimedes', a crane-like device designed to lift Roman ships out of the water and capsize them. While the existence of such a device is debated, historical accounts suggest that it played a significant role in the defense of Syracuse.

Archimedes is credited with developing and using compound pulley systems, allowing him to move exceptionally heavy objects with relatively little force. Accounts suggest he famously demonstrated this by single-handedly launching a fully laden ship.